Color in documents is the result of a combination of a limited set of colorants over a small area, in amounts selected to integrate to a desired color response. This is accomplished in many printing devices by reproducing separations of the image, where each separation provides varying amounts of a single primary colorant. When combined together with other separations, the result is a full color image.
For color images, a plurality of color separations are combined. Each color separation corresponds to a single colorant, and may be defined by a number of gray levels in excess of the capability of the printer. In such cases, each of the color separations is reduced from the input number of levels to the smaller output number of levels reproducible by the printer. The multiple color separations are combined together at printing to yield the final color print. Commonly, color documents are formed using cyan, magenta and yellow colorants or cyan, magenta, yellow and black colorants. A larger number or alternative colorants may also be used.
In printing documents, the desired gray level over an area is commonly achieved by halftoning, where image gray level variation is represented by placing greater or lesser numbers of ON pixels in a discrete area of the image. In one halftoning method, known as dithering or screening, over a given area having a number of gray separation pixels therein, a value representing the gray level of each separation pixel of an array of gray separation pixels within the area is compared to one of a set of preselected thresholds (the thresholds are stored as a dither matrix and the repetitive pattern generated by this matrix is considered a halftone cell) as taught, for example, in U.S. Pat. No. 4,149,194 to Holladay. For an area where the image is gray, some of the thresholds within the dither matrix will be exceeded, i.e., the image value at that specific location is larger than the value stored in the dither matrix for that same location, while others are not. In the binary case, the image pixels or cell elements for which the thresholds are exceeded might be printed as a maximum colorant value, while the remaining separation pixels are allowed to remain white, dependent on the actual physical quantity described by the data. The described halftoning method produces an output pattern that is periodic or quasi-periodic in the spatial coordinates.
Halftoning creates problems in color document reproduction where the repeating pattern of a screen through the image, when superposed over similar repeating patterns in multiple separations, can cause moire or other artifacts, particularly in printing systems with less than ideal registration between separations.
The artifacts caused by misregistration can be understood from simple examples. Assume for simplicity two separations having halftone screens with identical screen frequencies and angles. Printing those two separations on top one another in perfect registration will give a homogeneous color without periodic artifacts. If the second screen is spatially shifted with respect to the first screen, a strong shift in the output color will occur. Printing systems that are likely to have such a spatial displacement between the separations due to physical limitations are prone to color shift artifacts in the final prints.
A different type of artifact occurs if the printing system is likely to have a slight rotation between separations. In these instances, a color moire is formed, spatially progressing from one color to another. In another example, assume again for simplicity two separations having halftone screens having identical screen frequencies but different angles. Printing those two separations on top of one another in perfect registration will give a homogeneous color and, depending on the angle between the two separations, a high or low frequency moire. In situations where the angle is large (e.g.: 30.degree.) a high frequency moire occurs which is usually not to distracting, and in cases where the angle is small (e.g.: 2.degree.) a low frequency moire occurs which is usually distracting. If these two separations are printed shifted with respect to one another, no color shift is perceived in constant color areas, and no change in the moire frequency occurs. A halftone screen scheme using different angles for the different color separations is therefore less sensitive to a spatial displacement than a scheme using identical angles for all separations. If the two separations are printed with a change in the angle between the separations, the frequency and direction of the moire is altered and a non-objectionable moire might be changed to an objectionable moire.
There are always 2-way moire patterns between the color separations, but the angles are chosen to maximize the frequency of the moires (they are about 1/2 the screen frequency). These are the "rosettes" noted in magnified color halftones. This is true of both analog (photographic) and digital systems and is not a significant quality problem. Whenever a fourth color (black or "key") is included, there is another moire pattern, formed by a 3-way interaction between cyan, magenta and black. In analog systems, this moire is preferably positioned at zero frequency. In digital systems which use halftoning processes such as the Holladay rational angle screens, or the like, angles of exactly 15 degrees are not possible, so the 3-way moire is not quite at zero frequency. It should be noted that in systems using more than 4 colorants the equivalent argument holds for the dominant colorants of that system.
The color halftoning scheme using different angles for some or all of the color separations is common for applications that have slight misregistrations due to physical limitations. Accordingly, and with reference again to U.S. Pat. No. 4,149,194 to Holladay, the angle of the screen can be changed to generate similar screen patterns which do not strongly beat visually against each other, with the result the objectionable moire is reduced. Particularly critical are the angles between the most prominent colors, particularly cyan, magenta and black (if present). A common arrangement of rotated screen angles is 0.degree., 15.degree., 45.degree. and 75.degree. for yellow, cyan, black and magenta, respectively, in which case all separations are commonly halftoned using the same screen frequency, sometimes with the exception of yellow. However, objectionable patternings still occur. In general it can be said that periodic halftone schemes suffer from a combination of color moire and color shifts on misregistration, dependent on the actual scheme frequency, but is usually at a very objectionable low frequency.
An alternate method exists to suppress the 3-color moire described above. In this method, described in U.S. Pat. No. 5,394,252 to Holladay et al., one of the dominant colorant separations is replaced with a non-periodic or quasi-non-periodic screen, eliminating the 3-color moire.
It is important to note for the subsequent discussions that the input color (requested document color) is generally described as a 3 parameter quantity, e.g.: Xerox R,G,B as specified in the Xerox Color Encoding Standard, tristimulus values X,Y,Z, L*a*b*, scanner R,G,B etc. In the printing industry, rendering of a 3-separation image with more than 3 colorants, e.g. cyan (c), magenta (m), yellow (y), black (k), is achieved via a process of undercolor removal (UCR) and gray component replacement (GCR). This process, while most widely used for CMYK printing, can be generalized for an arbitrary choice and number (greater than 3) of colorants. Representing 3 input parameter quantities with e.g.: 4 output parameters, leaves one additional degree of freedom in selecting the 4 parameters. This patent describes a method to optimize the UCR/GCR process, and exploit the extra degree of freedom, to minimize moire.
It should be noted that the moire is caused by the unwanted absorption of the printing materials. With "perfect" inks, none of the described two or three color moires would occur with the exception of the moires formed through the k (black) separation. Looking at moire more closely, as noted above, two basic types of color moire influence print quality. The first type is the 2 color moire commonly found between yellow and cyan or yellow and magenta, etc. The second, normally more disturbing, moire is caused by the superposition of cyan, magenta, and black, or, in the case of more than 4 colorants, by the three dominant colorants present. For simplicity of the description and not for limiting the method, we will use the c,m,k case in the following. One interesting aspect of the moire is that it is not only a function of the spectral absorptance of the colorants, but also a rather direct function of the area coverage of any halftone dot used in reproduction of the image. To explain this, a simple 1-dimensional example can be used.
Assume the superposition of three transparencies, T.sub.c, T.sub.m and T.sub.k. The output is T=T.sub.c.multidot.T.sub.m.multidot.T.sub.k. Knowing that each transparency has the form of a halftone dot, i.e.: is a binary periodic function, it is noted that EQU T.sub.i (x, .lambda.).varies.a.sub.i (.lambda.)T.sub.i (x).varies.a.sub.i (.lambda.)[.SIGMA..sub.n b.sub.i,n cos(2.pi.f.sub.i x)] (1)
Where
a.sub.i (.lambda.) is the spectral absorbance of the i-th separation; PA1 T.sub.i (x) is the periodic screen pattern as a function of spatial location x; PA1 b.sub.i,n the n-th Fourier coefficients of the halftone screen of separation i; and PA1 f.sub.i is the frequency of the halftone screen of separation i; PA1 M(I.sub.n) is moire amplitude for the superposition of separations I.sub.n ; PA1 c, m, y and k, respectively denote reference to cyan, magenta, yellow and black or key separations; PA1 I.sub.n is the gray level input to the halftoner corresponding to separation n and PA1 I.sub.k (I.sub.c,I.sub.m,I.sub.y) indicates that the k-separation is determined as a function of the other separations.
Disregarding everything higher than first order, the equation can be simplified to: EQU T.varies.a.sub.c (.lambda.)a.sub.m (.lambda.)a.sub.k (.lambda.)[b.sub.c,0 +b.sub.c,1 cos(2.pi.f.sub.c x)][b.sub.m,0 +b.sub.m,1 cos(2.pi.f.sub.m x)][b.sub.k,0 +b.sub.k,1 cos(2.pi.f.sub.k x)] (2)
Equations (1) and (2) make it clear that if the individual transmittances would have no unwanted absorbtions, i.e.: a.sub.i (.lambda.).multidot.a.sub.i (.lambda.)=0, no moire would occur. Of all the cross-terms of Equation (2), only the term covering the three periodic components is involved in the 3-color moire. This moire component M can be written as EQU M.varies.b.sub.c,1 b.sub.m,1 b.sub.k,1 cos(2.pi.f.sub.c x) cos(2.pi.f.sub.m x) cos(2.pi.f.sub.k x) (3)
It is the regard for this moire component that will guide the GCR/UCR method described in this patent. The effect of this approach is that the degree(s) of freedom derived by representing a 3 parameter color quantity with more than 3 parameters will be used to fulfill boundary conditions totally or partially derived from the above mentioned moire considerations.
In contrast, conventional GCR/UCR strategies are a function of the minimum component of the requested color and potentially the overall lightness of the color. Commonly this means that while GCR/UCR is performed for darker colors, the UCR is set to zero for light colors, and colors with high chroma.
All of the references cited herein are incorporated by reference for their teachings.